A245548 Number of distinct sum representations of n by Fibonacci numbers with minimal digit sum.

1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1, 1, 2, 2, 3, 2, 1, 1, 3, 1, 4, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 5, 1, 1, 1, 3, 4, 1, 4, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 2, 2, 2, 3, 5, 2, 5, 2, 1, 1, 1, 1, 2, 3, 4, 3, 1, 1, 4, 1, 5

Offset

1,4

Comments

The digits are any nonnegative integers. The value of the minimal sum of digits is given by A007895. The sequence of those numbers where this sequence has value 1 is A256133.

Links

Table of n, a(n) for n=1..88.

M. Drmota and M. Gajdosik, The parity of the sum of digits function of generalized Zeckendorf expansions, The Fibonacci Quarterly, 36:1 (1988), pp. 3-19.

Example

a(12) = 3 because 12 = 8 + 3 + 1 = 8 + 2 + 2 = 5 + 5 + 2 has three distinct representations.

Maple

L:=[1, 2, 3, 5, 8, 13, 21, 34, 55]; LC:=[1, 1, 1, 2, 1, 2, 1, 1, 1]:LS:=[1, 1, 1, 2, 1, 2, 2, 1, 2]: for n from 10 to 88 do: ct:=0: ss:=n: sm:=n: b0:=1: b1:=2: b2:=3: b3:=4: b4:=trunc(n/L[5]): b5:=trunc(n/L[6]): b6:=trunc(n/L[7]):b7:=trunc(n/L[8]):b8:=trunc(n/L[9]):
> for n0 from 0 to b0 do:for n1 from 0 to b1 do: for n2 from 0 to b2 do:for n3 from 0 to b3 do: for n4 from 0 to b4 do: for n5 from 0 to b5 do: for n6 from 0 to b6 do:
> for n7 from 0 to b7 do:for n8 from 0 to b8 do: if n=n0*L[1]+n1*L[2]+n2*L[3]+n3*L[4]+n4*L[5]+n5*L[6]+n6*L[7]+n7*L[8]+n8*L[9] then ss:=n0+n1+n2+n3+n4+n5+n6+n7+n8:fi:
> if sm>ss then sm:=ss: fi: od:od:od:od:od:od:od:od:od:for n0 from 0 to b0 do:for n1 from 0 to b1 do: for n2 from 0 to b2 do:for n3 from 0 to b3 do:
> for n4 from 0 to b4 do:for n5 from 0 to b5 do:for n6 from 0 to b6 do:
> for n7 from 0 to b7 do:for n8 from 0 to b8 do:
> if n=n0*L[1]+n1*L[2]+n2*L[3]+n3*L[4]+n4*L[5]+n5*L[6]+n6*L[7]+n7*L[8]+n8*L[9] then st:=n0+n1+n2+n3+n4+n5+n6+n7+n8: if st=sm then ct:=ct+1: fi:fi: od; od:od:od:od:od:od:od:od: LS:=[op(LS), sm]: LC:=[op(LC), ct]: od: print(LC):

Crossrefs

Cf. A000045, A007895, A256133.

Sequence in context: A003647 A353352 A084217 * A025903 A175327 A101211

Adjacent sequences: A245545 A245546 A245547 * A245549 A245550 A245551

Keyword

nonn

Author

Patrick Okolo Edeogu, Oct 20 2015

Status

approved